A matrix-free implicit iterative solver for compressible flow problems. (English) Zbl 0838.76040

Summary: A procedure for solving nonlinear time-marching problems is presented. The nonsymmetric systems of equations arising from Newton-type linearizations are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Matrix-free techniques leading to reduction in storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES scheme is discussed. An automatic time-increment control strategy is developed to increase the stability of the time-marching process. High-speed flow computations demonstrate the effectiveness of these algorithms.


76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics